Prediction of sound absorption performance of fibers coming from cigarette butts using a phenomenological model

Abstract

This work deals with experimental and theoretical research about cellulose acetate fibers coming from cigarette butts. This waste, considered one of the most hazardous, numerous, and polluting waste all over the world, represents a high environmental risk. The possibility of using these fibers in sound-absorbing panels is evaluated. The acoustical properties are measured according to ISO 10534-2, and predicted using a phenomenological model over the frequency range from 100 Hz to 6400 Hz. This work includes the study of important non-acoustical properties for a better understanding of the porous structure. The Johnson-Champoux-Allard model provides good accuracy. The experimental results of the sound absorption spectrums show mean errors ranging from 1.1% to 9.0%. Moreover, it is possible to obtain non-acoustic properties of cellulose acetate fibers, which are difficult to obtain experimentally, using the Johnson-Champoux-Allard model and an inverse technique. The input parameters of this model are successfully obtained with low errors concerning the measurements (0.6–5.2% for porosity or 2.6–10.5% for flow resistivity). The results of the sound absorption spectrum at normal incidence of the cellulose acetate show very accurate predictions. The experimental results show values of sound-absorption coefficients close to 1.0 and sound absorption average ranging from 0.42 to 0.8. Therefore, these waste fibers are an alternative to the traditional porous absorbers, mainly composed of synthetic fibers or foams and petroleum-based resins.

Keywords

Sound absorption coefficient Cellulose acetate fiber Acoustic properties Phenomenological model Waste recycling

Introduction

In recent years, numerous developments have been carried out on using fibrous materials as sustainable sound absorbers in acoustic panels. These researches use different natural fibers such as coir,¹ date palm,^2-4 hemp,⁵ kenaf,⁶ yucca gloriosa⁷ and nettle,⁸ or recycled fibers such as wood and textile waste fibers,^9,10 polypropylene fibers,¹¹ and cellulose acetate fibers.^12,13 These works study the sound absorption performance and their non-acoustical properties. The sound absorption capacity of fibrous materials mainly depends on different non-acoustical properties. These properties are the bulk density, thickness, fiber size, porosity, tortuosity, airflow resistivity, surface impedance, compression rate, presence or absence of air-gap, and multilayer configurations. The effect of binding resins or mixtures of different materials must be taken into account.^14,15 These non-acoustical properties play an important role in the acoustical performance of porous materials.

The acoustical performance of sound fibrous absorbers can be evaluated by using sound-absorption models where the input parameters are the non-acoustical properties. The complexity degree of the model is based on the number of input parameters needed. Empirical models provide a relationship between the characteristic impedance and the characteristic wavenumber of the fibrous absorber. These models use the airflow resistivity as an input parameter and allow the prediction of the sound absorption coefficient. Some of these widely used models are Delany-Bazley (DBM),¹⁶ Mechel,¹⁷ Miki (MM),^18,19 Garai-Pompoli (GPM),²⁰ or Komatsu (KM)²¹ models. However, the presence of limiting factors governing their use, such as frequency range, porosity, or fiber diameter, makes it difficult to guarantee accurate results, mainly at low frequencies. Fibrous materials with complex internal structures require more complex models (a high number of input parameters) compared to fibrous materials with simple internal structures. The irregular structure and inhomogeneity of the fibrous materials are the main problems that limit the development of theoretical models to fit data obtained from the experimental measurements. Thermal and viscous effects must be taken into account to develop a model for sound propagation in porous materials for different pore shapes.²²

For this purpose, phenomenological models are used. These models need more input parameters to obtain the theoretical sound absorption coefficient in fibrous materials. In these models, the viscous and the thermal effects inside the fibrous material, when the air passes through it, are taken into account. These models include the Attenborough model,²³ the Johnson-Champoux-Allard model (JCA),^24,25 or the Johnson-Champoux-Allard-Lafarge model (JCAL),²⁶ among others.

Numerous works have attempted to theoretically study the physical parameters which affect the sound absorption coefficient. These works were based on different empirical or phenomenological models that predict the sound absorption mechanisms of porous materials as a function of their physical properties. Taban et al.² studied the acoustic performance of low-cost sound-absorbing panels with different thicknesses and densities through laboratory tests and modelling. Samaei et al.²⁷ proposed a quadratic model, based on four input parameters (sample thickness and density, binder content, and fiber to granule ratio), to optimize the sound absorption coefficient of new bio-based composites. These composites were made of kenaf fibers and rice husk, bonded with polyvinyl alcohol. The DBM and JCA models were used. The results showed superior prediction performance with the latter model. Samaei et al.²⁸ studied theoretically the acoustical performance of composites made of yucca and kenaf waste fibers, bonded with polyvinyl alcohol. These authors used different impedance models (DBM, GPM AND JCA), being the JCA model the most appropriate model for the prediction of the sound absorption coefficient. For this purpose, physical properties such as flow resistivity, tortuosity, viscous, and thermal characteristic lengths were calculated by an inverse technique. Samaei et al.²⁹ showed that the empirical DBM and GPM models efficiently predicted the sound absorption, with the absorption coefficient fitting well to the experimentally measured data. Samaei et al.³⁰ measured the sound absorption coefficient of Yucca Gloriosa natural fiber composites, and predicted it using the DBM and MM models. They found a close resemblance between the results of the models and the results obtained experimentally at low and medium frequencies. Samaei et al.³¹ studied the experimental and theoretical sound absorption coefficient of kenaf fibers when an alkaline process was applied to these fibers. They found that applying the Dunn-Davern model (DDM) and Nelder-Mead Simplex method provides a good fit between experimental and predicted results, reducing the error. In the work of Taban et al.³² sugar cane waste and corn husks were acoustically investigate using the DBM and Inverted DBM models with and Nelder-Mead Simplex method. The results obtained showed good prediction data according to experimental data.

Cigarette butts, made of cellulose acetate fibers, are one of the most common and numerous types of waste in the world. Their use as sound-absorbing material has been scarcely studied. The first studies were carried out by Gómez Escobar and Maderuelo-Sanz,³³ and Maderuelo-Sanz et al.¹² In these works, non-acoustical properties, such as porosity and flow resistivity, and sound absorption coefficient, for used and unused cigarette butts, were measured. In later works by the same authors, the effects on the sound-absorption coefficient of burnt regions and wrapping paper in the cigarette butts,³⁴ the initial conditioning of the fibers,³⁵ or the thickness or density of the fibers, were studied.³⁶ Likewise, Maderuelo-Sanz¹³ attempted to theoretically study the physical parameters which affected their sound absorption coefficient. In this work, the sound absorption coefficient of the cellulose acetate was predicted using four empirical models. The advantage of these models was based on the use of one easily measurable non-acoustical property, the airflow resistivity. However, other important non-acoustical properties, such as the tortuosity, and the viscous and thermal characteristic lengths, which are difficult to obtain experimentally were despised.

This work provides an experimental and theoretical investigation of the acoustic performance of cellulose acetate fibers using the Johnson-Champoux-Allard model. With this model, the complex internal pore structure is taken into account and the optimized non-acoustical properties (porosity, tortuosity, flow resistivity, viscous characteristic length, and thermal characteristic length) are obtained. Obtaining these properties is considered as the main gap with respect to this fibrous material. The experimental results show that this waste can be used as an alternative product to the traditional materials used for noise control applications like glass wool, foams, or rock wool inside commercial spaces like closed entertainment areas.

Materials

The material used in this work is cellulose acetate fibers coming from cigarette butts. To obtain it, cigarette butts of different brands are collected, the excess of tobacco is removed, and both, the outer and inner filter paper, is extracted by immersing the butts in distilled water. This solution is stirred in a magnetic heating stirrer for 1 h at 50°C. Subsequently, the process outlined by De Fenzo et al.^37,38 is followed. In this process, many of the chemicals impregnated in the cellulose acetate, such as metals (lead or nickel, among others), benzene, or nicotine are removed, as far as possible. This method is based on washing the butts in 96% ethanol twice and then drying them in an oven at 60°C for 1 h when a constant mass is obtained. Finally, they are crushed to expand the compressed fibers and sieved to remove possible fiber clumps (Figure 1). Afterward, the fibers are introduced into cylindrical molds with internal diameters of 29, and 100 mm, and pressed at 150 bar for 10 min. No bonding method is used. To evaluate the effect of increasing thickness in the sound absorption coefficient of the samples, with similar bulk density, samples with different thicknesses (30, 50, and 70 mm) are obtained. The reason for selecting these thicknesses is due to the typically thicknesses of traditional materials are ranging between 4 and 6 cm. For this reason, thicknesses similar to those commonly used in noise control applications are used.

Figure 1.

Full-scale and microscopic image of cellulose acetate fibers coming from cigarette butts.

Methodology

Non-acoustical properties

Open porosity

Open porosity, ϕ, influences the sound absorption capability of a sound porous absorber. The relationship between the volumes of the material frame and the interconnected pores defines the open porosity. In this work, open porosity is calculated non-acoustically through the next expression

Φ = 1 - \frac{ρ_{m}}{ρ_{s}}

(1)

where ρ_m is the bulk density of the sample (kg·m⁻³), and ρ_s is the skeletal density of the porous material (kg/m³). Real densities are obtained using a helium pycnometer (Quantachrome SPY-3) with a calibrated cell having a volume of 35.39 cm³. Each sample is measured three times, and the average value of the final real density is reported.

Flow resistivity

Flow resistivity, σ, is another critical non-acoustic parameter influencing the sound absorption properties of a porous absorber. It is directly related to the capability to absorb sound energy by the porous absorber. The resistance experimented by the air flowing through the porous material defines the flow resistivity. This physical property indicates how much sound energy is lost inside the porous absorber due to viscous and inertia effects when air passes through it.

In this work, the flow resistivity is obtained according to the method described by Ingard and Dear.³⁹ The flow resistivity is measured by using a cylindrical tube of diameter D closed with a loudspeaker at one end, and a rigid termination that closes the opposite end (Figure 2). The sound absorber, with thickness d, is placed near the middle of the tube. Two microphones are used to measure the sound pressure level. The first microphone is placed just at the front of the material sample (p₁). The second microphone is placed at the rigid termination of the tube (p₂). The wavelength of the sound wave, produced by the loudspeaker, has to be larger than 1.7D, and the distance between the sample and the rigid termination, L, has to be an odd number of quarter wavelengths, L+d = (2n-1)λ/4, where n = 1, 2, 3,… The flow resistivity of the sample is evaluated using the next equation

σ = \frac{ρ_{0} c_{0}}{d} {.10}^{L_{1} - L_{2} / 20}

(2)

where ρ₀ is the air density, c₀ is the sound propagation velocity in air, and L₁ and L₂ are the sound-pressure levels in front of the sample and at the rigid termination, respectively. Three samples are prepared for each different bio-composite, and the measurement process is repeated three times for each sample, being subsequently averaged.

Figure 2.

Airflow measurement system for Ingard and Dear indirect method .³⁹

Linear density

Linear density is a measure of the mass per unit length of a fiber. It is expressed in dtex,⁴⁰ which is the mass in grams per 10000 m of fiber. It is a measure of fiber fineness; the greater the thickness of the fibers, the greater the bending stiffness is. The linear density of the sample is evaluated using the next equation

d t e x = \frac{π ρ Φ^{2}}{4 \cdot 10^{- 6}}

(3)

where ρ is the bulk density of the sample (kg/m³) and Φ is the fiber diameter (≈0.0029 cm).¹³

Acoustical properties

Sound absorption measurements

To determine the normal incidence sound absorption coefficient of the samples, the test method specified in ISO 10534-2⁴¹ is applied. For this purpose, the Brüel and Kjær impedance tube type 4206 and the Brüel and Kjær PULSE signal analyzer are used. The measurement process is based on the use of a 10 cm diameter tube, for measurements in the frequency range 100–1600 Hz, and a 2.9 cm diameter tube, for the frequency range 500–6400 Hz. The Sound Absorption Average (SAA) index, defined in ASTM C423-17,⁴² is used to evaluate the sound absorption capacity of the samples. This index is useful for evaluating the performance of sound absorbers. The SAA is defined as the average of the sound absorption coefficients for the twelve one-third octave bands from 200 to 2500 Hz rounded to the nearest multiple of 0.01.

Johnson-Champoux-Allard model

The JCA model is the most commonly used semi-phenomenological model. It is derived from the Biot’s theory^43,44 which considers three dissipation mechanisms; viscous, thermal and structural, caused by the vibration of the skeletal in the porous medium. To take into account the highly complex porous structure at high frequencies, Johnson et al.²⁴ introduce the term “viscous characteristic length” in the effective density. Champoux and Allard²⁵ introduce the term “thermal characteristic length” in the effective bulk modulus. This model is used to acoustically characterize sound porous absorbers relating non-acoustic parameters involved in their microstructure. Five physical parameters are required as input parameters in this model: flow resistivity (σ), open porosity (ϕ), tortuosity (α_∞), the viscous characteristic length (Λ) and the thermal characteristic length (Λ^′). The dynamic density ρ_e(ω)²⁴ and the bulk modulus K_e(ω)²⁵ describe the dissipation of sound energy because of the viscous and thermal effects, respectively, due to the interaction of the air with the pores, and the frame of a fibrous sound absorber. These terms are written as follows

ρ_{e} (ω) = \frac{α_{\infty} ρ_{0}}{Φ} (1 + \frac{σ Φ}{i ω ρ_{0} α_{\infty}} \sqrt{1 + \frac{4 i α_{\infty}^{2} η ρ_{0} ω}{σ^{2} Λ^{2} Φ^{2}}})

(4)

K_{e} (ω) = \frac{\frac{γ P_{0}}{Φ}}{\frac{γ - (γ - 1)}{1 + \frac{8 η}{i Λ^{' 2} N_{p r} ω ρ_{0}} \sqrt{1 - \frac{i ρ_{0} ω N_{p r} Λ^{' 2}}{16 η}}}}

(5)

Z_{c} = {[ρ_{e} (ω) . K_{e} (ω)]}^{1 / 2}

(6)

k_{c} = ω {[\frac{ρ_{e} (ω)}{K_{e} (ω)}]}^{1 / 2}

(7)

Z_{s} = - i Z_{c} c o t (k_{c} . d)

(8)

α = 1 - {| \frac{Z_{s} - ρ_{0} c_{0}}{Z_{s} + ρ_{0} c_{0}} |}^{2}

(9)

where ρ_e(ω) is the effective density, K_e(ω) is the bulk modulus, Φ is the porosity, α_∞ is the tortuosity, σ is the flow resistivity, Λ is the viscous characteristic length, Λ^′ is the thermal characteristic length, ρ₀ is the air density, ω is the angular frequency, calculated by ω = 2πf, γ is the ratio of the specific heat capacity (≈1.4), P₀ is the atmospheric pressure (≈101320 N·m⁻²), η is the viscosity of the air (≈1.84∙10⁻⁵ Pas) and Npr is the Prandtl number (≈0.71).

To predict the normal-incidence sound absorption coefficient of the samples, obtained through equations (4)–(9), a best fit inverse methodology is used. This methodology is widely used by some authors.^27-32 The method is based on an iterative numerical method to minimize the differences between the experimental and the predicted sound absorption spectra, returning the non-acoustical parameters. The expression used is

F (α) = \sum_{n = 1}^{N} | α_{E x p} (f_{n}) - α_{J C A} (f_{n}) | \to m i n

(10)

where α_Exp is the experimental sound absorption spectrum, α_JCA is the theoretical sound absorption spectrum (obtained from JCA model for the combination of non-acoustical parameters), and f_n is the frequency in the range of 200–6400 Hz. The mean error, E_M, between the experimental and the theoretical sound-absorption spectra is obtained by the next expression

E_{M} = 100. \frac{\sum_{n = 1}^{N} | α_{E x p} (f_{n}) - α_{J C A} (f_{n}) |}{\sum_{n = 1}^{N} | α_{E x p} (f_{n}) |}

(11)

The frequency-dependent relative error E_f (%) between the measured (α_Exp) and the theoretical (α_JCA) sound absorption coefficient is obtained using the next expression

E_{f} = 100. \frac{| α_{E x p} - α_{J C A} |}{α_{E x p}}

(12)

Results and discussion

Non-acoustical properties

Open porosity is one of the key factors in the sound absorption performance of porous materials. Table 1 shows the open porosities. Small differences were observed between different samples. These values ranged from 0.957 to 0.987, showing that a significant decrease in bulk density led to a substantial increase in porosity, due to a higher number of voids in the material. Moreover, a decrease in tortuosity led to a decrease in the airflow resistivity of the samples.^27,28 The Ingard and Dear method³⁹ was used to obtain the flow resistivity. These values ranged from 3246 Pa s/m² to 34873 Pa s/m². It could be noted the relationship between the flow resistivity and the bulk density. An increase of bulk density led to a decrease in flow resistivity, so both were inversely proportional.⁴⁵

Table 1.

Physical properties of cellulose acetate samples studied in this work.

Sample	Thickness (cm)	Bulk density (kg/m³)	Porosity	Flow resistivity (Pa·s/m²)	Linear density (dtex)
M1	3	31.79	0.980	8429	0.210
M2	3	67.62	0.957	34873	0.447
M3	5	24.22	0.985	4872	0.160
M4	5	69.04	0.957	28524	0.456
M5	7	20.76	0.987	3246	0.137
M6	7	67.05	0.958	23604	0.443

Acoustical properties

The effect of thickness and bulk density on sound absorption coefficient

Figure 3 shows the sound absorption spectra for samples M2, M4 and M6 having different thicknesses (3, 5, and 7 cm, respectively), and similar bulk densities (67.62, 69.04, and 67.05 kg/m³, respectively), while a rigid-back wall was applied to them in the impedance tube. It could be observed by increasing the thickness of the samples, the sound absorption spectrum and the first interference maximum were shifted toward lower frequencies. The higher wavelength acoustic waves were absorbed in low frequencies when the porous medium had a considerable thickness. This effect was because the sound waves passed a longer path and the contraction of air molecules in the absorber increased.¹⁵ This effect meant a higher dissipative energy process inside the sample due to the viscous and thermal effects. Moreover, the first interference maximum showed lower amplitude.

Figure 3.

Effect of thickness on sound absorption coefficient for samples M2, M4 and M6.

Bulk density directly affects the acoustic absorption performance of porous materials. In porous materials having low densities, frictional losses are low and therefore, little energy conversion occurs. Figure 4 shows the sound absorption spectra for samples M1 and M2 with the same thickness, 3 cm, but within different bulk densities (31.79 and 67.62 kg/m³, respectively). The results obtained showed that increasing the bulk density of the samples led to the reduction of the porosity and therefore increasing the airflow resistivity of the samples. Therefore, this increase in the flow resistivity resulted in increasing the sound absorption coefficient. This effect occurred especially at low-frequency ranges.⁶ For this type of porous materials, the first maximum was expected near a wavelength λ = 4d, and the second maximum was expected not below a value corresponding to λ = 4d/3, being d the thickness of the sample.¹⁴ For the sample M3, the first and second maximums were expected at 1725 Hz and 5175 Hz, respectively, while the experimental values were 1748 Hz and 5200 Hz, respectively. For fibrous materials with low bulk densities, the tortuosity and flow resistivity were small; hence, a smaller dissipation of the acoustic wave energy inside the porous material was due to minimal internal friction when air passed through it.²⁷

Figure 4.

Effect of bulk density on sound absorption coefficient for samples M1 and M2.

Comparison with the JCA model

Table 2 shows the measured and the predicted open porosity and flow resistivity data for all samples studied in this work. The values of the predicted porosities were very similar to the porosities experimentally obtained. The relative error was ranging between 0.6% for sample M1 and 5.2% for sample M5. This work found slight differences in case of the predicted and experimental flow resistivities. The relative error was slightly higher, with relative errors between 2.6% and 10.5%. These differences were associated with possible errors in the experimental measurement of the flow resistivity. The values non-acoustical properties, tortuosity, viscous and thermal characteristic lengths, were found similar to other fibrous materials having high porosity values, and within the expected values.^2,27,45 In general, low tortuosity values were associated with highly porous materials.¹³

Table 2.

Experimental and predicted non-acoustical parameters for samples studied in this work.

Sample		Porosity	Flow resistivity (Pa·s/m²)	Tortuosity	Viscous characteristic length (μm)	Thermal characteristic length (μm)
M1	Experimental	0.980 ± 0.016	8429 ± 204	-	-	-
	Predicted	0.974	7808	1.042	87	175
	Relative error (%)	0.6	7.4	-	-	-
M2	Experimental	0.957 ± 0.012	34873 ± 914	-	-	-
	Predicted	0.992	37127	1.049	39	62
	Relative error (%)	3.7	6.5	-	-	-
M3	Experimental	0.985 ± 0.009	4872 ± 187	-	-	-
	Predicted	0.951	4359	1.039	127	201
	Relative error (%)	3.5	10.5	-	-	-
M4	Experimental	0.957 ± 0.021	28524 ± 747	-	-	-
	Predicted	0.981	29762	1.052	44	71
	Relative error (%)	2.5	4.3	-	-	-
M5	Experimental	0.987 ± 0.006	3246 ± 114	-	-	-
	Predicted	0.936	3337	1.041	179	214
	Relative error (%)	5.2	2.8	-	-	-
M6	Experimental	0.958 ± 0.026	23604 ± 506	-	-	-
	Predicted	0.971	24219	1.048	49	91
	Relative error (%)	1.4	2.6	-	-	-

Figure 5 shows the comparison between the experimental sound absorption spectra and the sound absorption spectra predicted by the JCA model, using as input parameters the optimized values of the non-acoustical parameters. In general, the values of sound absorption spectra, obtained from JCA model, were in good agreement with the sound absorption spectra obtained from experimental measurements.^27,28,46 The frequency-dependent relative errors between the measured and the theoretical sound absorption coefficient were below 3% for frequencies above 1000 Hz, as expected.^2,27,45 Some discrepancies were evident for frequencies below 1000 Hz, where the frequency-dependent relative errors were up to 10% for 560 Hz and 9% for 160 Hz for sample M4, or up to 9% for 160 Hz for samples M3 and M6. However, these errors were considered negligible with respect to the broader frequency range. The results obtained for the mean error of the sound absorption spectra ranged from 1.1% for the sample M1 to 9.0% for the sample M3. In this latter, the error was associated with the relatively high value of the predicted flow resistivity, as was mentioned above. Generally, the JCA model predicted the frequency of the peaks and the corresponding value of the sound absorption coefficient for the samples. It was obvious by looking at the mean error values that, due to the porosity and the flow resistivity measurements, and the inhomogeneity of the samples, the experimental measurements could suffer uncertainty. These deviations caused the differences between the experimental and the theoretical sound absorption spectra were observed.⁵ If we compare the results from the prediction sound absorption coefficients obtained in previous work,¹³ with the sound absorption coefficients obtained in the present work, it could be noted that the mean error obtained in both works were similar. In the work of Maderuelo,¹³ the mean error ranged from 0.8% to 8.7% while in this work the mean error ranged from 1.1% to 9.0%. However, it is worth noting that using the JCA model, it was possible to obtain non-acoustic properties, such as the tortuosity, and the viscous and thermal characteristic lengths, which are difficult to obtain experimentally, using an inverse technique. Therefore, it was possible to understand its porous structure, as well as the sound absorption coefficient.

Figure 5.

Experimental and predicted sound absorption spectra for cellulose acetate samples.

The sound absorption average (SAA), defined in ASTM C423-17,⁴² and the relative error, for the experimental and the predicted sound absorption coefficient, were calculated. The values of the experimental SAA ranged from 0.42 to 0.8 and the relative errors ranged from 1.4% to 3.8%. These results were according to other works.^6,13 It could be noted that the SAA increased as the thickness of the sample increased, as was expected. This effect was due to the interaction between the sound waves and the skeletal of the porous absorber was greater when increasing the thickness of the sample. The higher the thickness, the higher the thermal-viscous effects were because of friction, so the SAA was higher.

Conclusions

The work aimed to study the sound absorption performance of cellulose acetate fibers coming from cigarette butts by using a phenomenological model, the Johnson-Champoux-Allard model. Moreover, non-acoustic properties of this material were obtained by using a best-fit approach to fit experimental results. To achieve this objective six samples, having different non-acoustical properties, were manufactured and tested. The porosity and the flow resistivity of the samples, two of the most important non-acoustical properties affecting the sound absorption performance, were measured. Subsequently, the sound absorption coefficients of these samples were measured and the optimized non-acoustical properties (porosity, flow resistivity, tortuosity, viscous characteristic length and thermal characteristic length), as the input parameters for the Johnson-Champoux-Allard model, were calculated using an inverse method. However, in future works, the non-acoustical properties obtained by using the Johnson-Champoux-Allard model should be experimentally measured and compared with the non-acoustical properties obtained by the inverse methodology used in this work. Both sound absorption spectra, experimental and theoretical, were compared. It could be observed that sound absorption spectra predicted by the Johnson-Champoux-Allard model followed the trend of the experimental sound absorption spectra, providing high accuracy. The results from the predicted sound absorption coefficients obtained in this work, using the Johnson-Champoux-Allard model, were similar to the sound absorption coefficients obtained in other works, with a mean error ranging from 1.1% to 9.0%. The main advantage of using the Johnson-Champoux-Allard model was that important non-acoustic properties, which are difficult to obtain by experimental measurements, were obtained using an inverse method, and giving a better understanding of the porous structure of the material. In case of the predicted porosity and flow resistivity, the errors were ranging from 0.6% to 5.2% and 2.6%–10.5%, respectively. Future researches should study the acoustic properties of different composites made from cellulose acetate fibers, and different types and resin contents.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Francisco J García-Cobos

Rubén Maderuelo-Sanz

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